Tilt Grain Boundary Topology Induced by Substrate Topography

Synthesis of two-dimensional (2D) crystals is a topic of great current interest, since their chemical makeup, electronic, mechanical, catalytic, and optical properties are so diverse. A universal challenge, however, is the generally random formation of defects caused by various growth factors on flat surfaces. Here we show through theoretical analysis and experimental demonstration that nonplanar, curved-topography substrates permit the intentional and controllable creation of topological defects within 2D materials. We augment a common phase-field method by adding a geometric phase to track the crystal misorientation on a curved surface and to detect the formation of grain boundaries, especially when a growing monocrystal "catches its own tail" on a nontrivial topographical feature. It is specifically illustrated by simulated growth of a trigonal symmetry crystal on a conical-planar substrate, to match the experimental synthesis of WS₂ on silicon template, with satisfactory and in some cases remarkable agreement of theory predictions and experimental evidence.